Bootstrap for dependent Hilbert space-valued random variables with application to von Mises statistics
Year: 2013
Type: preprint
Abstract: Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their values in a Hilbert space. The random variables are assumed to be weakly dependent in the sense of near epoch dependence, where the underlying process fulfills some mixing conditions. As parametric inference in an infinite dimensional space is difficult, we show that the nonoverlapping block bootstrap is consistent. Furthermore, we show how these results can be used for degenerate von Mises-statistics.
Source: arXiv (Cornell University)
Authors: Dehling, H., Sharipov, O. Sh., Wendler, M.
Institution: Ruhr University Bochum
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949471979